The long-term objective of this work is to relate the function, design, and evolution of integrated biological systems to their underlying molecular determinants. As a result of the molecular advances in the past few decades, we are now in a position to examine the integrated behavior from an informed molecular perspective. For example, it is now well recognized that organisms regulate expression of their genome by means of a diverse repertoire of molecular mechanisms. By contrast, little is known about the forces that lead to the selection or maintenance of a specific mechanism for the regulation of a given set of genes in a particular organism. Is this process random, or is it governed by rules? The answer to this question is important for understanding the evolution of gene regulation. It also is important for redirecting normal expression for biotechnological purposes or correcting pathological expression for therapeutic purposes. This project is concerned with developing specific aspects of a general theory of gene regulation and with analyzing the systemic behavior of particular gene circuits and biochemical networks. The specific aims are to elucidate (1) natural selection of gene circuits for inducible systems in prokaryotes, (2) design of gene circuits for repressible systems in prokaryotes, (3) rules for the modality of gene control in eukaryotic cells, and (4) systemic influence of the gene products in biochemical systems. The methodology emphasized in these studies is mathematical and computer-assisted analyses because of their unique ability to systematically relate integrated function and design of organizationally complex biological systems to their molecular elements. The general outline for the analysis in each case is as follows: Specific models based on known or suspected molecular elements and interactions are formulated; the integrated behavior of these models is analyzed and compared according to several different criteria for functional effectiveness; the results of the analysis are interpreted in terms of optimal designs for specific functions; and, finally, the biological significance of the results is addressed and predictions are made for experimental testing. This project will help to create a more rational basis for predicting the integrated behavior of complex biological systems. Accurate predictions of this nature will be necessary if we are to understand more fully the normal systemic processes of homeostasis, growth and development, or their pathological manifestations such as metabolic diseases, developmental abnormalities and cancer.